Several analytic inequalities in some $Q-$spaces

Abstract

In this paper, we establish separate necessary and sufficient John-Nirenberg (JN) type inequalities for functions in $Q_{\alpha }^{\beta }({\mathbb{R}}^n)$ which imply Gagliardo-Nirenberg (GN) type inequalities in $Q_{\alpha }({\mathbb{R}}^n).$ Consequently, we obtain Trudinger-Moser type inequalities and Brezis-Gallouet-Wainger type inequalities in $Q_{\alpha }({\mathbb{R}}^n).$

13 pages submitted